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Spatially distributed functional data are prevalent in many statistical applications such as meteorology, energy forecasting, census data, disease mapping, and neurological studies. Given their complex and high-dimensional nature,…

Statistics Theory · Mathematics 2024-02-06 Suneel Babu Chatla , Ruiqi Liu

We consider the problem of multivariate density deconvolution when the interest lies in estimating the distribution of a vector-valued random variable but precise measurements of the variable of interest are not available, observations…

Methodology · Statistics 2016-12-06 Abhra Sarkar , Debdeep Pati , Bani K. Mallick , Raymond J. Carroll

We consider the problem of sampling from a posterior distribution arising in Bayesian inverse problems in science, engineering, and imaging. Our method belongs to the family of independence Metropolis-Hastings (IMH) sampling algorithms,…

Machine Learning · Computer Science 2026-05-19 Youguang Chen , George Biros

Surveys often ask respondents to report nonnegative counts, but respondents may misremember or round to a nearby multiple of 5 or 10. This phenomenon is called heaping, and the error inherent in heaped self-reported numbers can bias…

Applications · Statistics 2015-09-15 Forrest W. Crawford , Robert E. Weiss , Marc A. Suchard

Recently emerging large-scale biomedical data pose exciting opportunities for scientific discoveries. However, the ultrahigh dimensionality and non-negligible measurement errors in the data may create difficulties in estimation. There are…

Methodology · Statistics 2022-10-28 Xin Ma , Suprateek Kundu

In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…

Statistics Theory · Mathematics 2024-02-27 Han Cheng Lie , T. J. Sullivan , Aretha Teckentrup

We present a novel approach to estimating discrete distributions with (potentially) infinite support in the total variation metric. In a departure from the established paradigm, we make no structural assumptions whatsoever on the sampling…

Statistics Theory · Mathematics 2020-10-16 Doron Cohen , Aryeh Kontorovich , Geoffrey Wolfer

Estimating the Generalization Error (GE) of Deep Neural Networks (DNNs) is an important task that often relies on availability of held-out data. The ability to better predict GE based on a single training set may yield overarching DNN…

Machine Learning · Computer Science 2022-07-20 Angus Galloway , Anna Golubeva , Mahmoud Salem , Mihai Nica , Yani Ioannou , Graham W. Taylor

Transfer learning is a key component of modern machine learning, enhancing the performance of target tasks by leveraging diverse data sources. Simultaneously, overparameterized models such as the minimum-$\ell_2$-norm interpolator (MNI) in…

Machine Learning · Statistics 2026-01-19 Yeichan Kim , Ilmun Kim , Seyoung Park

This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…

Machine Learning · Statistics 2013-10-04 Peter Kovesarki , Ian C. Brock

Frequently, empirical studies are plagued with missing data. When the data are missing not at random, the parameter of interest is not identifiable in general. Without additional assumptions, we can derive bounds of the parameters of…

Methodology · Statistics 2018-09-12 Zhichao Jiang , Peng Ding

The inferential models (IM) framework provides prior-free, frequency-calibrated, posterior probabilistic inference. The key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown…

Statistics Theory · Mathematics 2016-01-26 Ryan Martin , Chuanhai Liu

Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is…

Machine Learning · Statistics 2017-01-17 Song Mei , Yu Bai , Andrea Montanari

Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…

Statistics Theory · Mathematics 2025-06-10 Rong Tang , Yun Yang

Deep neural networks often fail when deployed in real-world contexts due to distribution shift, a critical barrier to building safe and reliable systems. An emerging approach to address this problem relies on \emph{disagreement discrepancy}…

Machine Learning · Computer Science 2025-12-08 Neil G. Marchant , Andrew C. Cullen , Feng Liu , Sarah M. Erfani

Multivariate pattern analyses approaches in neuroimaging are fundamentally concerned with investigating the quantity and type of information processed by various regions of the human brain; typically, estimates of classification accuracy…

Machine Learning · Statistics 2016-10-11 Charles Y. Zheng , Yuval Benjamini

Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…

Information Theory · Computer Science 2022-12-05 James Melbourne , Saurav Talukdar , Shreyas Bhaban , Mokshay Madiman , Murti V. Salapaka

Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…

Machine Learning · Statistics 2017-11-07 Ho Chung Leon Law , Christopher Yau , Dino Sejdinovic

In this paper, we explore bounds on the expected risk when using deep neural networks for supervised classification from an information theoretic perspective. Firstly, we introduce model risk and fitting error, which are derived from…

Machine Learning · Computer Science 2024-10-08 Binchuan Qi

In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse…